Half the Sum: Finding the Area of Trapezoids

About This Resource

A complete Grade 6 math pack on the area of trapezoids. Students discover the formula A = ½(a + b)h by joining two identical trapezoids into a parallelogram, identify the parallel sides and the height, and find areas from labeled diagrams and word problems. Includes slides, a lesson plan, worksheet, quiz, homework, A5 flashcards, a rubric, Word files and answer keys.

Overview

A trapezoid has one pair of parallel sides, a and b, and a height h measured at right angles between them. Two identical trapezoids, one turned upside down, fit together to make a parallelogram with base a + b and height h. So the area of one trapezoid is half of that: A = ½(a + b)h. Students identify the parallel sides and the perpendicular height, use the formula with labeled diagrams and solve real-world problems such as the area of a garden bed.

Resource Details

Subject: Math
Topic: Area of Trapezoids
Category: Shapes & Geometry
File Type: PDF
File Size: 354.1 KB
Published: 14 Nov 2026
Downloads: 0

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Grade 6 (ages 11–12) 55 minutes Geometry measurement formulas problem solving

Learning Objectives

Identify the parallel sides and the perpendicular height of a trapezoid.
Explain where the formula A = ½(a + b)h comes from.
Calculate the area of trapezoids in diagrams and word problems.

How to Use This Resource

Show two identical paper trapezoids. Ask: "Can you make a shape whose area you already know?"
Derive the formula with the slides, then do activities 1 and 2 together.
Students complete activities 3 to 6. Use the quiz and send the homework page home.

Classroom Activity Ideas

Cut and join: students cut out two identical trapezoids and form a parallelogram.
Spot the height: students mark the height on trapezoids drawn at different angles.
Design a garden: students design a trapezoid-shaped garden bed with a given area.

Differentiation

Support: give a formula card and diagrams with the height already marked. Challenge: find a missing parallel side or height when the area is given.

Assessment

Use the worksheet and quiz to check calculations. Use the rubric for the explanation in activity 6.

Teacher Tips

The most common mistake is using a slanted side as the height. Insist that the height is perpendicular to the parallel sides. Encourage students to add the parallel sides first, then multiply by the height and halve.

What's Included

11-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (6 words with meanings and examples)
Student worksheet (6 activities)
Quiz / assessment (3 parts)
Homework practice page
Printable flashcards: 6 A5 picture cards (separate PDF)
Assessment rubric (4 levels)
Lesson slides (editable PowerPoint)
Editable Word version of all student pages
Complete answer key (also as a separate PDF)

Additional Files

Lesson Slides (PPTX)
Editable Student Pages and Lesson Plan (DOCX)
A5 Flashcards (PDF)
Answer Key (PDF)

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